If it is true that Christ saw his cross primarily as a way to communicate his love and mercy to the world, then his command to us to take up our cross means primarily that we take up that way in which we can communicate love and mercy to our neighbor.
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The thing Moderns, Medievals, and Ancients call “science” proceeds from the self-evident to the proven. The primary self evident thing is an account corresponding to what a word means. Before we have this account, science is impossible, and it is only to the extent that we have this account that we can have the science. The name for an account corresponding to what a word means is “a definition”.

Definitions are first of all articulations of what the name means. Definitions can be more or less perfect, and the sorts of definitions that are most perfect are those that we first give the name “definition” to, but nonetheless, we must start with definition, for we must start with a word that has an intelligible meaning, and this intelligible meaning of a word is the first sense of definition.

The divergence of sciences, therefore, must happen at the level of definition, for identical accounts of a word cannot lead to divergent properties processing from the posited essence of the thing. In my experience, the contemporary sciences define things in terms of how they are measured- Einstein famously said that for a physicist, to define means to have some measurement that can be empirically verified. This metrical account is closely alled to the “functional account” the definition that best allows for manipulation of something, or its use (this kind of account is most common in mathematics, which defines numbers as things that can be put into an equation). What is common to most all sciences is that they are all to willing to reject how everyday language would define things, in order to glorify “the scientific understanding” of things.

The inevitable consequence of functional definitions and metrical definitions, if they are taken as the best or only kind of definition, is the death of speculative science and the desire to know things for their own sake. The common element of metrical and functional definitions is that they are human artifacts, and no human artifact is more noble than man. But speculative sciences concern things better than man.

Certain contemporary math texts refer to boxes, cubes, and prisms as “cylinders”, since the volume of each can be expressed as “area of the base times the height”, and it they go on to define pyramids as “cones” since they are one third of the base times the height. So too, physicists define “acceleration” in such a way as to include both speeding up and slowing down. LIkewise “zero velocity”, is nothing more than a certain numerical value in an equation. Examples of this sort of thing abound in the metrical sciences.

My suspicion has been for a while that all the paradoxes and oddities of the contemporary sciences are paradoxes of measurement- a confusion between what a thing is and how it is measured. The scientist only allows meaning to measurement, and he is ready to dismiss language at the slightest sign of conflict. There is also the fact that the sciences can call all things the same so long as they are values to be “plugged into” an equation, regardless of how diverse the things might be in ordinary language.

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The first division in mathematics is between the sort of math which is done most perfectly when done without thought, and the sort of math that is done most perfectly when thought is fully active. If you have to think about what 9 times 6 is, you have room to perfect your calculation skills. If you’re giving a proof in mathematics, any thoughtless presentation is imperfect. To the extent that the sciences are mathematical, this same distinction applies.
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Mathematics is the body of knowledge which gives us the greatest certainty, and so it is the model for us of what all sciences should be. If we view all Mathematics as a tool, we can do no other than view science as a tool; if we view math as nothing other than the manipulation of its subject matter, we will view all science as manipulation of the subject matter; if we view all math as art, we view all science as an art. Our view of science cannot be higher than our view of math, for mathematics simply is the body of knowledge about which we have the greatest certainty, and we know we are most certain of it.

The loss of liberal mathematics in modern times was a devestation. There is no measure for the things we lost. In a very real sense, we lose all science when we lose mathematics: what remains and calls itself science is really an art that treats nature as pure matter to be informed by the scientist. The only joy or intrinsic worth to such a “science” is the banal fascination of a game or hobby. Mathematics, when taught as a speculative science and liberal art, provides us an irreplaceable grasp of what it means to know something for its own sake, and through this we can know the joy of contemplation- which is the true life of science- the highest and most noble life a man can live, in this life or any other.

Again, mathematics is the indispensible first grasp we have of science, and there is some sense in every man that science ought to be the rule and measure of human life. We use the word “science” to describe the most precise, objective, penetrating, and sure kind of knowledge. But too often this natural respect for science gets contracted and distorted so as to apply only to physical sciences based on disprovable hypotheses and verified by experiment. This leads to the conclusion- commonly heard and experienced by all- that man, when he is most certain about something (having science) in fact has only probability.

The modern mind, having lost the paradigm of mathematics, divides all learning into the sciences and the humanities. The common element in both of these is their uncertainty and groundlessness. A student goes to a science class and learns that nothing can count as a science unless it is disproveable; then he goes to a humanities course and be told that the whole goal of humanities is to “enter into the great conversation” or “learn the various ways that people have struggled with the great questions”. Gone is any sense of paideia, of that sense awareness in man that knowledge is the sort of thing that should be sought for its own sake; and that the goal of an educated man was to tell the difference between the things he was certain of, and not certain of. One of the best signs of the educated man is that he knows what needs to be proven, and what doesn’t need to be proven. But without mathematics, we can’t even be expected to know what proof means.

-I have heard people compliment certain philosophers because “at least they believe in an objective moral standard and that truth exists”. Huh? This is no compliment. It’s like complimenting someone who calls himself a doctor because he believes that health exists, or complimenting someone who calls himself a mechanic because he recognizes nothing other than that it is possible to fix certain cars.

-The way most people define the word “science” makes it impossible for geometry or arithmetic to be sciences. Neither of these studies is based on falsifiable hypotheses that are verified by experiment. No one releases his findings on the Pythagorean theorem that they might be independently verified, nor does he need to run many confirming tests to establish that the theorem is a law. The same can be said for Logic and Grammar.

-It is a common complaint that Scholastic Philosophy is too dry, formulaic, and uninspiring. The same charge is leveled against the Apostles Creed. Profound understandings of truth do not usually come from first reads but from contemplation- unless you’re reading Euclid.

-What is not known directly by sense is known by analogy, causality, and negation- and negation is the most indispensible of these, for our imagination tends to distort and make dull the things beyond sense. We imagine the angelic hierarchy is a set of glowing points in black space; we imagine heaven is a place where we stare at the sun all day; we imagine the spirit of a man as a vapor shaped like a man. We perfect our knowledge of immaterial things by negating what we imagine them to be. This should be obvious: “immaterial” is a negation.

-Euclid’s fifth postulate gives a condition under which a triangle comes to be. By negating this triangle, we prove the existence of parallel lines, which are themselves known by the negation of contact (they will not touch).

– I have never known of an Algebra student who could define Algebra.

-From the second paragraph of an Algebra book: “a line is a straight curve”. This was soon followed by a picture of “a straight angle”, and an account of a number as “an idea”. And we wonder why kids can’t get this stuff. This is not just a matter for high school pedagogy- if we have some of these thoughts in our own minds, we need to uproot them.

-I sat in a class on Hegel once and thought: I wish I could trust what the teacher is saying. I had a gut feeling that I could trust some of what he was saying, and not other things. I could foresee the labor of having to sift through all the things he said. Then I imagined what it would be like to hear some class from the mouth of someone who I completely trusted, and whose thought I knew would never let me down. Then I imagined what it would be like to hear sit in a class and listen to an angel, who could not err in any natural knowledge. Last of all, I imagined what it would be like to sit in a class and listen to God, who could not err on any point at all, and whose words would be totally dependable. All of a sudden, I remembered that this is what revelation is.

Anything that Aristotle, Plato and St. Thomas agree on should be a philosophical slam-dunk. Like:

Consider the points of agreement in Logic, or the process of coming to know:
-the words which man speaks reveal the essences of things which are grasped by his mind

-the essence of something is grasped and articulated most perfectly by the one who expresses it in a definition.

-one must carefully distinguish the various meanings of words

-Man grasps certain things immediately, without having to reason, and he knows them with certainty.

-Geometry is a science which provides the greatest certainty and ease of learning for man, and it therefore should be learned first in time- from Euclid.

-The universal cannot be simply reduced to the particulars it contains.

-the highest knowledge is the knowledge which is sought for its own sake, as opposed to for being for the sake of something else.

-Man is capaple of attaining a knowledge that cannot be otherwise.

-Man’s most perfect knowledge, or science, can be instansiated in knowledge of Geometry and of what is now called “philosophy” or “metaphysics”

or as regards The knowledge of nature:

-Man comes to know all things he knows by the possession of their form- i.e. knowledge is having the form of another.

-sense knowledge is in some way of indeterminite and unknowable things, because the things we sense are in some way unknowable in themselves.

-Nature is defined in reference to motion, and this motion makes things difficult to understand.

-to exist as a man is to exist through a soul, and this soul is the principle of life.

-The soul is unified to the body at least as a mover to moved, and it continues to know and to be conscious after death, which is the separation of the soul from the body.

-The human soul is demonstrably immaterial.

-Man is capable of proving the existence of a supernatural being called God on the basis of the existence of moving things (Plato does so in the Laws).

In Metaphysics
-Goodness has a certain primacy over all, inasmuch as goodness is an end.

-God is supremely good, and as such is the end of all things.

-God is one, supremely living, and benevolent, creator of the world, neither coming to be nor passing away.

-Evil is not a being, but the lack of being.

-Goodness is communicative of itself.

Regarding Ethics

-Virtue can be called the greatest perfection of human life.

-Though many different action can be called good, there are not many moralities that can be called good.

-The goal of human life is union with God, and a certain divinization.

-Adultery, impiety to divinity, sophistry, not helping people in the same way one wishes to be helped, homosexuality, indifference or hatred of the highest things, intemperance, cowardice, and sodomy are wrong, always and in every instance.

-Man will live an eternal, conscious life after this one

-Human nature is weak, and attains to virtue only with struggle.
________

*When I speak of Plato, I’m including his main protagonist/master, Socrates.

The form of the Socratic method is well known: the question and answer format that strives to manifest “what the student already knows”. The proper term of the Socratic method, however, is a definition. To notice this explains some difficult aspects of the Socratic method:

-Definitions are not “proven”, for they are not something known in addition to the name, but only clearer grasps of what the name means. We don’t prove that a circle is a figure such that all points are equadistant from some point (called a center), nor do we prove that nouns are names, nor that verbs are words that signify with time. For this reason, the Socratic method is best understood as showing what someone “already knows”, for we only come to a clearer grasp of what we already had confusedly in the name itself.

-Some definitions are unattainable. This is in fact true of most definitions we seek, and it is definitely true of any search to define God, who is the cause of all causes and the root of all knowability. Hence Socratic skepticism makes sense. If wisdom means comprehending the very essence of God (i.e. knowing exhaustively), then wisdom is impossible, in this life or any other.

-For the above reason, it makes sense to refer to the philosophical life as a sort of “perpetual questioning” or “endless search”. I can’t add quickly enough, however, that the Socratic search is the absolute contradiction of the Marxist or revolutionary search. The Socratic search, when it is perpetual, is a perpetual learning, and therefore a perpetual knowing- for learning cannot be understood apart from coming to know. The marxist or revolutionary search is a continual refutation, a rejection and denial. The Socratic search is one that recognizes the essential orientation of the human mind, through words, to the essences of things; the revolutionary search negates the essential orientation of the mind, through words, to the essences of things.

-At some point, the definer using the Soratic method will have to appeal to “something that is known to all”. This is why the contrary of the Socratic method is the one who insists that nothing is “known to all”- usually because he will appeal to what is today called “diversity”, or “scholarly research”- i.e. anything that emphasises the manyness and diversity of opinion as such and for its own sake. The exaultation in the sheerly many is called “sophistry”.

I have never heard anyone deny the existence of God on the basis of the death of Socrates, the death of Christ, or the martyrdom of Christians. As far as I can tell, to do so is psychologically impossible- one can utter words like “how can God exist when St. Polycarp is burned, or St. Therese of the Little flower dies from tuberculosis?” But to say so carries no force within the mind- the words are unpursuasive and produce no assent. Such statements, in other words, are absurd. I take this absurdity as a given.

The argument from evil, then, can only produce assent when the evil is not viewed in union to a Christian life, or a virtuous life. No one questions the existence of God when confronted with the great evils that befell Socrates, or Christ, or Cato, or The Little Flower. It is not simply the case that the evils that befell these persons cannot be harmonized with the argument from evil- their deaths even seem to contest or deny the argument from evil. These evils are too bound up with meaningfulness, with a sense of order, with glory- what are they, even, being both so manifestly evil and so manifestly a cause of glory in the lives in which they occured?

Evil is not a sufficient cause or occasion for the argument from evil. The only sufficient cause is a particular kind of evil: a human life that is viewed apart from meaning. May no evil befalling me give one occasion to doubt the existence of God.
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St. Thomas is called “the Angelic Doctor” primarily because of the loftiness of his intellect and the purity of his life, but also because he simply wrote quite a lot about angels. St. Thomas clearly saw the world with which we are most familiar- the world of man and family and politics and the stars- as being a very small thing in comparison to the angelic universe.

This angelic universe, so very present to the consciousness of Thomas Aquinas, is a universe that is best understood by us as unknown. We best understand the angelic universe by informed negation because our imagination tends to soil any positive grasp of the angels and their universe with absurd images of toga-clad-long-haired-blonde-girls with wings floating on clouds or in space (ugh); to grasp how absurd this is, imagine if a dog, who had only heard about his master, were to imagine him as a dog walking upright on his hind legs. In truth, there would be far more truth in the dog’s imagining than in our imagining angels.

For many reasons, the study of angels has fallen on hard times. This absence of angels from the mind can only be a cause of distortion and corruption of our understanding of the world. Without awareness of the angels, we tend to loose perspective on the smallness of our world, on the inferiority of our intellectual power, on the comparitive lowness of our natural dignity, and on the nature of our own intellectual operation and life. We loose also important aspects of the supernatural order- the doctrine of guardian angels, for example, but also we miss how profound and shocking the incarnation is- how could he possibly choose to die for us? we barely exist!

(The above argument fails since it assumes that there was some intrinsic goodness in man could compell the incarnation- yet it is not so, for “while we were yet enemies, Christ died for us” yet man is still quite humbled by contemplation of the angels.)

But the greatest thing we miss from failing to contemplate the angels is the very knowledge that we attain by contemplating them, for in this contemplation of natures higher than our own, our mind becomes in a certain sense a friend of the angels, and it enters, as much as possible, into the world of pure intelligence which is both above us, and yet is at the same time the measure of what is most ourselves. Inasmuch as we are bodily, we are measured by time, but inasmuch as we are immaterial, we are measured by sempiternal existence above all passing, lack and corruption- every person lives in the angelic universe even now. For this reason, contemplation of the angels both humbles us and shows us our highest dignity.

The greatest setback to the study of the angels is that no one has shown how to understand them given newer understandings of the material world. To understand many angelic attributes, St. Thomas would argue by proportion: as corruptible bodies are to incorruptible bodies, so material beings are to angels. An example of this sort of reasoning is found here. St. Thomas often argues things from the old cosmology, but very often there is a solid argument left if one ignores the argument from the old cosmology, but not so with the angelic arguments. To be clear, one can prove the existence of the angels, and some of their properties, by means of arguments that do not appeal to the old cosmpology, as St. Thomas often does. Bt the loss of the old cosmology caused far more damage to the thomistic study of angels than to any other comparable part of thomistic science. We can only understand the angels by some analogy to things seen (this is the only way we can understand anything unseen-even ourselves) but we have lost the old things which were thought to provide an analogue to angels.